Date/Time : 28 Jul 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Vilas Winstein , University of California, Berkeley

This is part 2 of a two-talk series. We will discuss some recent results on the limiting Gaussian nature of fluctuations of various observables under exponential random graph models; in particular, we obtain quantitative error bounds via Stein’s method. A key novelty is that our results apply in the low-temperature parameter regime which has previously been unexplored and requires new methods. These include the application of novel concentration inequalities derived from carefully analyzing the mixing behavior of relevant Markov chains.

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Date/Time : 25 Jul 2025 16:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Vilas Winstein , University of California, Berkeley

This is part 1 of a two-talk series. We will introduce exponential random graph models, which are exponential tilts of Erdős–Rényi models by functions which increase or decrease the number of certain small subgraphs (e.g. triangles). We will also discuss relevant tools for studying these modelThis is part 1 of a two-talk series. We will introduce exponential random graph models, which are exponential tilts of Erdős–Rényi models by functions which increase or decrease the number of certain small subgraphs (e.g. triangles). We will also discuss relevant tools for studying these models, such as large deviations principles, mixing results, and concentration inequalities.s, such as large deviations principles, mixing results, and concentration inequalities.

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Date/Time : 21 Apr 2025 10:00
Venue : S17 #04-04 (SR3)
Speaker : Weijun XU, Peking University

Many stochastic PDEs arising from natural probabilistic models are classically “wrong” in the sense that they involve products between distributions. This type of ill-posedness has been existing even in ODEs. Ito’s theory of SDEs is probabilistic in nature. There is a lack of analytic stability, as can be seen from the existence of Ito-Stratonovich corrections.

We start from an old idea by Terry Lyons, now known as rough paths, that aimed to understand the nature of the analytic ill-posedness in SDEs. We will then see how these early attempts are gradually developed into a quite complete picture today for singular PDEs (regularity structures and para-controlled distributions). We shall focus on one particular example of singular SPDE, the 2D generalised parabolic Anderson model, to illustrate the coherence of this series of ideas.

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Date/Time : 17 Apr 2025 16:30
Venue : S17 #05-11 (SR5)
Speaker : Weijun XU, Peking University

Many stochastic PDEs arising from natural probabilistic models are classically “wrong” in the sense that they involve products between distributions. This type of ill-posedness has been existing even in ODEs. Ito’s theory of SDEs is probabilistic in nature. There is a lack of analytic stability, as can be seen from the existence of Ito-Stratonovich corrections.

We start from an old idea by Terry Lyons, now known as rough paths, that aimed to understand the nature of the analytic ill-posedness in SDEs. We will then see how these early attempts are gradually developed into a quite complete picture today for singular PDEs (regularity structures and para-controlled distributions). We shall focus on one particular example of singular SPDE, the 2D generalised parabolic Anderson model, to illustrate the coherence of this series of ideas.

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Date/Time : 14 Apr 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Weijun XU, Peking University

Many stochastic PDEs arising from natural probabilistic models are classically “wrong” in the sense that they involve products between distributions. This type of ill-posedness has been existing even in ODEs. Ito’s theory of SDEs is probabilistic in nature. There is a lack of analytic stability, as can be seen from the existence of Ito-Stratonovich corrections.

We start from an old idea by Terry Lyons, now known as rough paths, that aimed to understand the nature of the analytic ill-posedness in SDEs. We will then see how these early attempts are gradually developed into a quite complete picture today for singular PDEs (regularity structures and para-controlled distributions). We shall focus on one particular example of singular SPDE, the 2D generalised parabolic Anderson model, to illustrate the coherence of this series of ideas.

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Date/Time : 24 Feb 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Shota Osada, Kagoshima University

In this talk, we will consider the construction of $\mu$-reversible diffusion processes for a given point process $\mu$ on  $\mathbb{R}^d$. Specifically, we will discuss the Dirichlet form method to construct distorted Brownian motion on configuration spaces. For Poisson point processes, this corresponds to an infinite number of independent Brownian motions on $\mathbb{R}^d$. For correlated point processes, the interaction between particles is characterized by a function called the log-derivative, which describes the force exerted on one particle by the others. In previous results, the construction of diffusion processes using Dirichlet forms and their characterization using log-derivatives have been treated separately. In this talk, I will introduce that the existence of a logarithmic derivative implies the closability of the Dirichlet form. 

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Date/Time : 24 Feb 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Shuhei Shibata, Kyushu University

We study the classical law of iterated logarithm for centered continuous Gaussian processes. Also, we introduce one of the asymptotic behavior of a non-Markovian stochastic process called elephant random walk as an application.

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Date/Time : 14 Feb 2025 11:00
Venue : S17 #05-11 (SR5)
Speaker : Benoît Corsini,

In this talk, I will present an upcoming result regarding the local evolution of Prim’s algorithm seen as a random process on graphs. To do so, I will start by introducing the concept of local limit for a sequence of graphs, before defining Prim’s algorithm and showing its relation to the minimum spanning tree. Finally, I will combine these two concepts to provide a representation of the limit, in particular its relation to invasion percolation and the percolation levels of a graph.

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Date/Time : 14 Feb 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Luca Makowiec, National University of Singapore

We will introduce Random Spanning Trees in Random Environment (RSTRE), a disordered system on spanning trees that interpolates between the Uniform Spanning Tree (UST) and Minimum Spanning Tree (MST) measures. Our primary goal is to study how local and global observables of the RSTRE depend on the inverse temperature beta. Of particular interest is the diameter of a (typical) spanning tree, as it is the first step towards establishing convergence to a non-trivial scaling limit. Furthermore, for the RSTRE on the complete graph with uniform disorder, we discuss a sharp transition of the local limit of the RSTRE to either the UST or MST local limit. This stands in contrast to our conjectured smooth transition of the diameter when beta is inside the so-called intermediate regime.

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